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The design matrix contains data on the independent variables (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a dependent variable). The theory relating to such models uses the design matrix as input to some linear algebra : see for example linear regression.
Many regression methods are naturally "robust" to multicollinearity and generally perform better than ordinary least squares regression, even when variables are independent. Regularized regression techniques such as ridge regression , LASSO , elastic net regression , or spike-and-slab regression are less sensitive to including "useless ...
Hypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests. In multivariate tests the columns of Y are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix.
Missing data and attempts to resolve missing data (i.e. using the subject’s mean for non-missing data) can raise additional problems in RM-ANOVA. 4. MLM can also handle data in which there is variation in the exact timing of data collection (i.e. variable timing versus fixed timing). For example, data for a longitudinal study may attempt to ...
The earliest regression form was seen in Isaac Newton's work in 1700 while studying equinoxes, being credited with introducing "an embryonic linear aggression analysis" as "Not only did he perform the averaging of a set of data, 50 years before Tobias Mayer, but summing the residuals to zero he forced the regression line to pass through the ...
The multilevel regression is the use of a multilevel model to smooth noisy estimates in the cells with too little data by using overall or nearby averages. One application is estimating preferences in sub-regions (e.g., states, individual constituencies) based on individual-level survey data gathered at other levels of aggregation (e.g ...
In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. [1] It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.
A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. [1] This term is distinct from multivariate linear regression , which predicts multiple correlated dependent variables rather than a single dependent variable.